In rectangle ABCD, the diagonals meet at point O. Find side BC if the perimeter of triangle AOD

In rectangle ABCD, the diagonals meet at point O. Find side BC if the perimeter of triangle AOD is 18 cm and AC + BD = 22 cm.

AC and BD are the diagonals of the rectangle, which means they are equal and intersect in the middle. Find half of the diagonal (segment AO):

AC = 22/2 = 11 cm;

AO = AC / 2 = 11/2 = 5.5 cm;

AO = OD;

Let’s find the unknown side of the triangle AOD:

AD = 18 – 5.5 – 5.5 = 7 cm;

This side of the rectangle is opposite to the BC side, and the opposite sides of the rectangles are equal.

Answer: BC = 7 cm.